vs_mram: Variable Selection via the Multivariate Regression...

In MRAM: Multivariate Regression Association Measure

Variable Selection via the Multivariate Regression Association Measure

Description

Select a subset of \bf X which can be used to predict \bf Y based on T_n.

Usage

vs_mram(y_data, x_data)

Arguments

y_data	A n \times d matrix of responses, where n is the sample size.
x_data	A n \times p matrix of predictors.

Details

vs_mram performs forward stepwise variable selection based on the multivariate regression association measure proposed in Shih and Chen (2025). At each step, it selects the predictor with the highest conditional predictability for the response given the previously selected predictors. The algorithm is modified from the FOCI algorithm from Azadkia and Chatterjee (2021).

Value

The vector containing the indices of the selected predictors in the order they were chosen.

References

Azadkia and Chatterjee (2021) A simple measure of conditional dependence, Annals of Statistics, 46(6): 3070-3102.

Shih and Chen (2026) Measuring multivariate regression association via spatial sign, Computational Statistics & Data Analysis, 215, 108288.

See Also

mram

Examples

library(MRAM)

n = 200
p = 10

set.seed(1)
x_data = matrix(rnorm(p*n),n,p)
colnames(x_data) = paste0(rep("X",p),seq(1,p))

y_data = x_data[,1]*x_data[,2]+x_data[,1]-x_data[,3]+rnorm(n)
colnames(x_data)[vs_mram(y_data,x_data)] # selected variables

## Not run: 

n = 500
p = 10

set.seed(1)
x_data = matrix(rnorm(p*n),n,p)
colnames(x_data) = paste0(rep("X",p),seq(1,p))

# Linear
y_data = matrix(0,n,2)
y_data[,1] = x_data[,1]*x_data[,2]+x_data[,1]-x_data[,3]+rnorm(n)
y_data[,2] = x_data[,2]*x_data[,4]+x_data[,2]-x_data[,5]+rnorm(n)
colnames(x_data)[vs_mram(y_data,x_data)] # selected variables

# Nonlinear
y_data = matrix(0,n,2)
y_data[,1] = x_data[,1]*x_data[,2]+sin(x_data[,1]*x_data[,3])+0.3*rnorm(n)
y_data[,2] = cos(x_data[,2]*x_data[,4])+x_data[,3]-x_data[,4]+0.3*rnorm(n)
colnames(x_data)[vs_mram(y_data,x_data)] # selected variables

# Non-additive error
y_data = matrix(0,n,2)
y_data[,1] = abs(x_data[,1]+runif(n))^(sin(x_data[,2])-cos(x_data[,3]))
y_data[,2] = abs(x_data[,2]-runif(n))^(sin(x_data[,3])-cos(x_data[,4]))
colnames(x_data)[vs_mram(y_data,x_data)] # selected variables

## End(Not run)

MRAM documentation built on Jan. 8, 2026, 1:08 a.m.